One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

A dynamic subgrid‐scale eddy viscosity model

We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095000462

On the identification of a vortex

http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

/pdf/turbulence-and-the-dynamics-of-coherent-structures-i-1o6o6m60fm.pdf

Turbulence and the dynamics of coherent structures. I. Coherent structures

The precise dynamics of breakdown in pipe transition is a century-old unresolved problem in fluid mechanics. We demonstrate that the abruptness and mysteriousness attributed to the Osborne Reynolds pipe transition can be partially resolved with a spatially developing direct simulation that carries weakly but finitely perturbed laminar inflow through gradual rather than abrupt transition arriving at the fully developed turbulent state. Our results with this approach show during transition the energy norms of such inlet perturbations grow exponentially rather than algebraically with axial distance. When inlet disturbance is located in the core region, helical vortex filaments evolve into large-scale reverse hairpin vortices. The interaction of these reverse hairpins among themselves or with the near-wall flow when they descend to the surface from the core produces small-scale hairpin packets, which leads to breakdown. When inlet disturbance is near the wall, certain quasi-spanwise structure is stretched into a Lambda vortex, and develops into a large-scale hairpin vortex. Small-scale hairpin packets emerge near the tip region of the large-scale hairpin vortex, and subsequently grow into a turbulent spot, which is itself a local concentration of small-scale hairpin vortices. This vortex dynamics is broadly analogous to that in the boundary layer bypass transition and in the secondary instability and breakdown stage of natural transition, suggesting the possibility of a partial unification. Under parabolic base flow the friction factor overshoots Moody’s correlation. Plug base flow requires stronger inlet disturbance for transition. Accuracy of the results is demonstrated by comparing with analytical solutions before breakdown, and with fully developed turbulence measurements after the completion of transition.

https://www.pnas.org/content/pnas/112/26/7920.full.pdf

Osborne Reynolds pipe flow: Direct simulation from laminar through gradual transition to fully developed turbulence.

A numerical technique for computations of turbulent flows is described. The technique is based on B-splines and allows grid embedding in physically significant flow regions. Numerical tests, which include solutions of nonlinear advection-diffusion equations and computations of flow over a circular cylinder at Reynolds numbers up to 300, indicate that the method is accurate and efficient. In computations of flow over a cylinder, the lift, drag, and base suction coefficients agree well with existing experimental data and previous numerical simulations.

B-spline method and zonal grids for simulations of complex turbulent flows

Analysis of stability and accuracy of finite-difference schemes on a skewed mesh

: As a first step to understand the compressibility effects, interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by three-dimensional time-dependent direct numerical simulations. In addition, linear analysis was used to study interaction of isotropic turbulence with shock waves of a wide range of strengths. The effects of the fluctuation Mach number M sub t and the average Mach number M sub 1 superscript u of the upstream turbulence on turbulence statistics were investigated. Both numerical simulations and linear analyses of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy (TKE) and transverse vorticity components are amplified, and turbulent length scales are decreased. The predictions of the linear analyses compare favorably with simulation results for flows with M sub t < M sub 1 superscript U-1, which suggests that the amplification mechanism is mainly linear.

/pdf/interaction-of-isotropic-turbulence-with-a-shock-wave-1i5vyke0qw.pdf

Parviz Moin

Papers

Osborne Reynolds pipe flow: Direct simulation from laminar through gradual transition to fully developed turbulence.

B-spline method and zonal grids for simulations of complex turbulent flows

Analysis of stability and accuracy of finite-difference schemes on a skewed mesh

Interaction of Isotropic Turbulence with a Shock Wave

Numerical aspects and implementation of a two-layer zonal wall model for LES of compressible turbulent flows on unstructured meshes